This invention relates to communication systems employing polynomial-generated error-correction encoding, and more particularly relates to encoding and decoding techniques for reducing the number of logic gates used in such systems.
Polynomial-generated error-correction coding, such as Reed-Solomon coding, requires encoders and decoders with many gates. Most of the gates are allocated to Galois field multiplier structures. By using certain field polynomials for the Galois field multiplier structures, the number of gates can be reduced. However, the field polynomial which enables gate reduction is frequently incompatible with other parts of the encoder or decoder system which are made with commercially available parts. As a result, there is a need for a system of converting a code compatible with one field polynomial to a code compatible with another field of polynomial which enables a reduction in the number of gates used in the encoders or decoders. This invention addresses the problem and provides a solution.
The preferred embodiment is useful on a communication system employing polynomial-generated error-correction coding using encoders and decoders which comprise logic gates. In such an environment, according to a first embodiment of the invention, code words of a first form compatible with a first field polynomial selected to reduce the number of the logic gates are generated, preferably by an encoder. Code words of a second form compatible with a second field polynomial are decoded, preferably by a decoder. The code words of the first form are converted to code words of the second form before the code words of the second form are decoded.
According to a second embodiment of the invention, code words of a first form compatible with a first field polynomial are generated, preferably by an encoder. Code words of a second form compatible with a second field polynomial selected to reduce the number of logic gates are decoded, preferably by a decoder. The codes words of the first form are converted to code words of the second form before the code words of the second form are decoded by the decoder.
Using the foregoing techniques, systems employing field polynomials selected to reduce the number of logic gates can be made compatible with systems also employing encoders or decoders that use other field polynomials. As result, polynomial-generated error-correction coding systems can be customized to increase efficiency and reduce overall costs.